The city is tripling the number of public housing apartments it intends to put under private management — to 62,000 — under a program officials say will help fund nearly $13 billion in renovations over the next 10 years.

The announcement Monday by Mayor Bill de Blasio came just five months after the city boosted the number of apartments in the program — from 15,000 to 20,000 — and followed a successful implementation of the initiative at 1,400 public housing units in Far Rockaway.

The Queens project, which converted the units to federally funded Section 8 housing under a program known as “Rental Assistance Demonstration,” generated $560 million in upgrades for one development alone, according to city officials.

“It’s time for big, systemic changes,” the mayor said at the Betances Houses in the South Bronx. “We believe this approach can work on a much bigger scale.”